A gas fills the right portion of a horizontal cylinder whose radius is 5.80 cm. The initial pressure of the gas is 2.64 x 105 Pa. A frictionless movable piston separates the gas from the left portion of the cylinder that is evacuated and contains an ideal spring, as the drawing shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 27.1 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A gas fills the right portion of a horizontal cylinder whose radius is 5.80 cm. The initial pressure of the gas is \(2.64 \times 10^5\) Pa. A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as illustrated. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 27.1 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring.

**Diagram Explanation:**

The diagram below the text visualizes a horizontal cylinder. On the right side, it is filled with gas, represented by a pattern of blue dots. A piston separates the gas from the left side of the cylinder, which is empty and contains an ideal spring. The spring is initially unstrained. A pin is placed on the piston to hold it in position.

**Interactive Section:**

The interactive section at the bottom has a field where users can input a "Number" and select "Units" measured in N/m (Newtons per meter) to determine the spring constant.
Transcribed Image Text:A gas fills the right portion of a horizontal cylinder whose radius is 5.80 cm. The initial pressure of the gas is \(2.64 \times 10^5\) Pa. A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as illustrated. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 27.1 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring. **Diagram Explanation:** The diagram below the text visualizes a horizontal cylinder. On the right side, it is filled with gas, represented by a pattern of blue dots. A piston separates the gas from the left side of the cylinder, which is empty and contains an ideal spring. The spring is initially unstrained. A pin is placed on the piston to hold it in position. **Interactive Section:** The interactive section at the bottom has a field where users can input a "Number" and select "Units" measured in N/m (Newtons per meter) to determine the spring constant.
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